Emergent Thiemann coherent states in the near-kernel sector of quantum reduced loop gravity
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| Format: | Preprint |
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2026
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| _version_ | 1866917508335796224 |
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| author | Mäkinen, Ilkka Sahlmann, Hanno Sherif, Waleed |
| author_facet | Mäkinen, Ilkka Sahlmann, Hanno Sherif, Waleed |
| contents | We study the near-kernel sector of the Hamiltonian constraint operator in the one-vertex model of quantum reduced loop gravity using variational Monte Carlo methods with neural quantum states. The analysis is based on the symmetric Hamiltonian containing both Euclidean and Lorentzian contributions, and on the variational minimization of the positive quadratic operator $\hat{\mathcal Q}=\hat C \hat C^\dagger$ in truncated Hilbert spaces with spin cutoff up to $j_{\mathrm{max}}=1001$. The resulting near-kernel states are found to organize into three qualitatively distinct classes. At low cutoffs, we find solutions that do not factorize across the three edge degrees of freedom. At larger cutoffs, we find two different factorized branches, both described to very high accuracy by products of one-edge wavefunctions but localized in different spin regimes. One of these branches is matched with near-unit fidelity by reduced Thiemann coherent states, providing evidence for an emergent semiclassical organization of the near-kernel sector. The other is likewise strongly factorized, but its one-edge factors are not well described by the same coherent-state family. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_18625 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Emergent Thiemann coherent states in the near-kernel sector of quantum reduced loop gravity Mäkinen, Ilkka Sahlmann, Hanno Sherif, Waleed General Relativity and Quantum Cosmology High Energy Physics - Theory Computational Physics We study the near-kernel sector of the Hamiltonian constraint operator in the one-vertex model of quantum reduced loop gravity using variational Monte Carlo methods with neural quantum states. The analysis is based on the symmetric Hamiltonian containing both Euclidean and Lorentzian contributions, and on the variational minimization of the positive quadratic operator $\hat{\mathcal Q}=\hat C \hat C^\dagger$ in truncated Hilbert spaces with spin cutoff up to $j_{\mathrm{max}}=1001$. The resulting near-kernel states are found to organize into three qualitatively distinct classes. At low cutoffs, we find solutions that do not factorize across the three edge degrees of freedom. At larger cutoffs, we find two different factorized branches, both described to very high accuracy by products of one-edge wavefunctions but localized in different spin regimes. One of these branches is matched with near-unit fidelity by reduced Thiemann coherent states, providing evidence for an emergent semiclassical organization of the near-kernel sector. The other is likewise strongly factorized, but its one-edge factors are not well described by the same coherent-state family. |
| title | Emergent Thiemann coherent states in the near-kernel sector of quantum reduced loop gravity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Computational Physics |
| url | https://arxiv.org/abs/2605.18625 |